In addition to the Canadian cars, the recall covers about 298,000 U.S. vehicles, 3,400 in Mexico and about 900 outside of North America.
The Italian-American automaker said the recall covers 2013 through 2016 model year automatic transmission Dart cars and that the defect could prevent drivers from shifting vehicles into park.
Fiat Chrysler said it is not aware of any crashes or injuries related to the issue but has several thousand reports of related repairs to vehicles.
Fiat Chrysler said it will replace the transmission side shifter cable bushing, but did not say when repairs will be ready.
Fiat Chrysler ended production of the Dart in 2016.